Scientific notation

Scientific notation is a convenient way to deal with very large or very small numbers.

It provides an easier way to write numbers and make multiplication and division of very large or very small numbers a lot easier.
A number is in this format if we can write it as:

a × 10n

with 1 ≤ a < 10 and n is an integer.

1 ≤ a < 10 means that a is a number greater than or equal to 1, but less than 10.

Thus, a can be 1,2,3,4,5,6,7,8, and 9

Scientific notation
Let's start with something simple. Write 500 in this useful notation:

500 = 5 × 100 = 5 × 102

You can also claim as we saw before that there is a decimal point after 0 and write 500.0

Then, move the decimal point 2 places to the left between 5 and 0 to get 5.000, which is the same as 5.

Since you moved it two places to the left, you know that your exponent is 2.

Your base is always 10

Thus, 500 = 5 × 102

A few more examples showing how to convert a number into scientific notation.


Example #1: Convert 75000 into scientific notation.

75000 = 75000.0

Move the decimal point 4 places to the left between 7 and 5.

We get 7.5000, which is the same as 7.5

Since we moved it 4 places to the left, your exponent is 4 and your base is still 10.

Thus, 75000 = 7.5 × 104

Sometimes, instead of moving your decimal point to the left, you have to move it to the right as the following example demonstrates:

When you move your decimal point to the right, your exponent is negative.

Example #2: 0.002

Move your decimal point 3 places to the right after the 2 to get 0002. and 0002. is the same as 2. or 2

Since you had to move it 3 places to the right, your exponent is -3 and the base is still 10

Thus, 0.002 = 2 × 10-3

Example #3: 0.000065

Move decimal point 5 places to the right

The answer is 6.5 × 10-5

Example #4: 650000

Move decimal point 5 places to the left

The answer is 6.5 × 105

Scientific notation quiz. See how well you can convert numbers to scientific notation.

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